introduction how does a bat work? implications for bat design wood aluminum summary
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#521, September 28, 1960. How Would a Physicist Design a Bat? The Physics of the Baseball-Bat Collision Alan M. Nathan University of Illinois at Urbana-Champaign [email protected]. Introduction How Does a Bat Work? Implications for Bat Design Wood Aluminum Summary. - PowerPoint PPT PresentationTRANSCRIPT
AAAS Symposium on The Science of Baseball February 18, 2000 Page 1
How Would a PhysicistHow Would a PhysicistDesign a Bat?Design a Bat?
The Physics of the Baseball-Bat CollisionThe Physics of the Baseball-Bat Collision
Alan M. NathanAlan M. NathanUniversity of Illinois at Urbana-ChampaignUniversity of Illinois at Urbana-Champaign
[email protected]@uiuc.edu IntroductionIntroduction How Does a Bat Work?How Does a Bat Work? Implications for Bat DesignImplications for Bat Design
Wood Aluminum
Summary#521, September 28, 1960
see http://www.npl.uiuc.edu/~a-nathan/pob
AAAS Symposium on The Science of Baseball February 18, 2000 Page 2
Introduction: Description of Ball-Bat CollisionIntroduction: Description of Ball-Bat Collision
forces large (>8000 lbs!) time is short (<1/1000 sec!) ball compresses, stops, expands kinetic energy potential energy bat affects ball….ball affects bat
GOAL: maximize vf
vf 105 mph x 400 ft x/vf = 5 ft/mph
What aspects of collision lead to large vf?
AAAS Symposium on The Science of Baseball February 18, 2000 Page 3
• vf depends on initial ball and bat speed
vf = P vball + (1+P)vbat
* bat speed much more important!
* collision very inefficient
• Where does the energy go?
* recoil/rotation of bat
* dissipation in ball
* vibrations in bat
How Does a Bat Work?How Does a Bat Work?Maximizing vMaximizing vff
Typical numbers:
P = .22 (1+P) = 1.22 90 + 70
105 mph
AAAS Symposium on The Science of Baseball February 18, 2000 Page 4
Where Does the Energy Go?1. Recoil/Rotation of Bat
.
Translation:
Mball/Mbat
.Rotation:Mball z2/I
CM .
z
Note:• Bat speed depends on
these• See Terry Bahill’s Talk
Important Bat Parameters:
• mass (inertia)
• location of CM
• distribution about CM
(“rotational inertia”)
AAAS Symposium on The Science of Baseball February 18, 2000 Page 5
Where Does the Energy Go?2. Dissipation in Ball
Coefficient Of Restitution: “bounciness” of ball Bounce ball off massive hard surface
COR2 = hf/hi
For baseball, COR .5 3/4 energy lost! Changing COR by .05 changes V by 7 mph (35 ft!)
Important Point: the bat matters too!
AAAS Symposium on The Science of Baseball February 18, 2000 Page 6
Where Does the Energy Go?2. Dissipation in Ball
Energy shared between ball and bat depends on relative compressibilities
Ball is inefficient: 25% returned Wood Bat
Ebat/Eball ~0.02 80% restored COReff = 0.50-0.51
Aluminum Bat Ebat/Eball ~0.10 80% restored COReff = 0.55-0.58
“trampoline effect”
~10% larger!
tennis ball/racket
Important Bat Parameters:• compressibility• elasticity
AAAS Symposium on The Science of Baseball February 18, 2000 Page 7
Collision excites bending vibrations in bat Ouch!! Thud!! Sometimes broken bat Energy lost lower vf
Lowest modes easy to find by tapping Reduced considerably if
collision at node fn < 1/collision time
Where Does the Energy Go?3. Vibrations in Bat
Fundamental: 170 Hz
1st overtone: 560 Hz
-16
-12
-8
-4
0
4
8
12
16
0 5 10 15 20 25 30 35
-16
-12
-8
-4
0
4
8
12
16
0 5 10 15 20 25 30 35
nodes
Important Bat Parameters:• stiffness• shape
AAAS Symposium on The Science of Baseball February 18, 2000 Page 8
Putting it all together...
0
0.1
0.2
0.3
0.4
10 15 20 25 30
vf (m/s)
distance from knob (inches)
rigid bat
flexible bat
CM node
• 1 m/s collision with stationary wood bat
• Louisville Slugger R161 (33”, 31 oz)
• calculation…amn• data…Rod Cross
Conclusions:
• rigid model works poorly• vf = rigid value at node
Essential physics understood
AAAS Symposium on The Science of Baseball February 18, 2000 Page 9
Putting it all together...
• Under realistic conditions…• 90 mph, 70 mph at 28”• no data yet…..
20
40
60
80
100
16 20 24 28 32
vf (mph)
distance from knob (inches)
flexible bat
rigid bat
Louisville SluggerR161 (33", 31 oz)
CM nodes
-20
0
20
0 2 4 6 8 10
v (m/s)
t (ms)
Motion of Handle
24”
27”
30”
Possible “sweet spots”
1. Maximum of vf (28”)
2. Node of fundamental (27”)
3. Center of Percussion (27”)
Handle barely moves
by time ball leaves bat!
AAAS Symposium on The Science of Baseball February 18, 2000 Page 10
Designing a Bat
vf = P vball + (1+P)vbat• Goals
* vf large at maximum* vf vs. impact location broad
• Opposing tendencies…* to optimize P mass far from hands* to optimize vbat mass close to hands
• From our analysis….* vf insensitive to size, shape of bat far from impact
• Therefore….* make barrel fat and long* make handle feel comfortable * adjust taper to move CM
AAAS Symposium on The Science of Baseball February 18, 2000 Page 11
Optimizing a Wood Bat
-2
0
2
4
6
8
10
12
0 5 10 15 20 25 30
R161 (33”, 31 oz)
Modified bats with same mass
20
40
60
80
100
16 20 24 28 32
vf (mph)
distance from knob (inches)
uniform
R161 + Modifications
Preliminary Conclusions: 1. Can’t do much to affect wood bat within constraints allowed by rules, weight2. Long, fat barrel; thin handle seems best
AAAS Symposium on The Science of Baseball February 18, 2000 Page 12
Wood versus Aluminum
• Length and weight “decoupled”* Can adjust shell thickness* Fatter barrel, thinner handle
• More compressible* COR larger
• Weight distribution more uniform* Easier to swing* Less rotational recoil* More forgiving on inside pitches
• Stiffer for bending* Less energy lost due to vibrations
0
20
40
60
80
100
16 20 24 28 32
vf (mph)
distance from knob (inches)
wood
aluminum-1
aluminum-2
wood versus aluminum
AAAS Symposium on The Science of Baseball February 18, 2000 Page 13
Summary/ConclusionsSummary/Conclusions
Physics of ball-bat collision largely understood bat can be well characterized ball is less well understood
Essential parameters for bat design known mass and mass distribution compressibility and elasticity stiffness and shape
Hillerich & Bradsby probably know this already!